Local variational differential operators in field theory

We develop a new calculus for local variational differential operators where the action of higher-order operators on local functionals does not lead to indefinite quantities like $\delta(0)$. We apply this formalism to the Batalin–Vilkovisky formulation of local general gauge field theory and to its $Sp(2)$-symmetrical generalization. Its relation to a semiclassical expansion is also discussed.